Nautical Solver | Prismatic Coefficient (CP)

Length L (m) ⓘ

Midship area A_M (m²) ⓘ

Have ∇ or Δ? ⓘ

I don’t have A_M. Compute from C_M, B, T

Result

CP = —

Enter inputs to compute.

Report: Prismatic Coefficient (Direct)

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Provide C_B & C_M directly, or leave one/both blank and give enough geometry to derive them.

C_B (optional)

If blank, we can compute from ∇/(L·B·T).

C_M (optional)

If blank, we can compute from A_M/(B·T).

L for CB (m)

B (m)

T (m)

Have ∇ or Δ?

A_M (m²) (optional)

If blank, compute via C_M·B·T below.

B (m) for C_M

T (m) for C_M

Result

CP = —

Enter inputs to compute.

Report: Prismatic Coefficient (From C_B & C_M)

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Result

∇ (Simpson) = — m³

A_M (chosen) = — m²

CP = —

Enter areas & station details.

Report: Prismatic Coefficient (Offsets)

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Empirical Target

Froude number: —

Suggested target: CP ≈ — (range —)

Heuristic for early sizing—refine with geometry.

Report: Prismatic Coefficient (Empirical)

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What is the Prismatic Coefficient (CP)?

The prismatic coefficient (CP) is a dimensionless hull-form parameter that describes how a ship’s underwater volume is distributed along its length. It compares the actual displaced volume to a prism formed using the midship section area and the ship’s length.

Definition

CP is defined as the ratio between the displaced volume and the product of the midship section area and the chosen length reference:

CP = ∇ / (A_M × L)

where ∇ is the underwater volume, A_M is the immersed midship section area, and L is typically taken as Lpp or LWL.

Relationship with other hull coefficients

The prismatic coefficient is closely related to the block coefficient (CB) and midship coefficient (CM) through the relationship:

CP = CB / CM

This relationship highlights how CP isolates the longitudinal distribution of volume, while CB reflects overall hull fullness and CM describes the midship section shape.

Typical CP values by vessel type

Typical CP ranges depend strongly on vessel speed and hull form. The values below are indicative for conventional displacement vessels:

Fast craft & patrol vessels: 0.55 – 0.65
Container ships & Ro-Ro vessels: 0.60 – 0.70
General cargo vessels: 0.62 – 0.72
Bulk carriers & tankers: 0.70 – 0.80

Engineering significance

CP is a key parameter in resistance and powering analysis. For a given speed range, there exists an optimal CP that minimizes wave-making resistance. Slender, high-speed vessels typically favor lower CP values, while fuller, slower ships require higher CP values.

During preliminary design, CP is often selected empirically based on Froude number and later refined through detailed hull geometry and resistance calculations.

Limitations and correct use

CP alone does not define hull resistance or propulsion power.
It must be evaluated together with CB, CM, and wetted surface area.
Results depend on consistent use of length reference (Lpp vs LWL).
Empirical CP targets are suitable for early design only.
Final CP values should be validated using offsets and hydrostatics.

Related calculators

The prismatic coefficient is typically evaluated alongside the following hull-form and performance parameters:

Block Coefficient (CB) – overall hull fullness indicator.
Midship Coefficient (CM) – midship section shape factor.
Displacement Calculator – converts hull geometry into displacement.
Wetted Surface Area (WSA) – required for resistance estimation.
Holtrop–Mennen Resistance – estimates calm-water resistance from hull parameters.

Tip: Keep L choice consistent. CP should be between 0 & 1 for realistic hulls.